Geophysical data such as microscopic images, (e.g. thin sections), wellbore images, and seismic data volumes are noisy. Geologic models of reservoir properties are uncertain. Techniques for measuring and analyzing contiguous features in these types of data can be extremely sensitive to such uncertainty. The current approach to measuring contiguous features in volumetric data is based on a technique called region growing, sometimes called seed detection. See, for example, Russ, John C., The Image Processing Handbook, Second Edition, CRC Press 1995. The user specifies (1) a starting voxel, v0, assumed to be located in some feature of interest, and (2) a voxel eligibility criterion, E, which defines whether a voxel should be considered part of the feature of interest. E is usually a function of the voxel's observed value. The region of interest, R, is initialized to be the specific starting voxel. A computer algorithm then iteratively examines all voxels adjacent to R and adds them to R if they satisfy E. When no more voxels can be added to the region, the algorithm stops, having identified all voxels that satisfy E and are connected to v0 by other satisfying voxels. Thus, to be included in the region, voxels have to be both eligible (by satisfying E) and connected to v0 by at least one path through other eligible voxels. A petroleum industry example of this technique is described in U.S. Pat. No. 5,757,663 to Lo, et al. The application described by the Lo patent treats connectivity in a reservoir model, not in observed data such as seismic data, and does not address the issue of uncertainty in the model.
A frailty with the region growing approach lies in the fact that noise in the voxel values can produce erroneous decisions with respect to E. Geographically narrow features can be cut by a small amount of noise that prevents the addition of otherwise qualified voxels. Adjacent, but distinct, features can be joined by a small amount of noise that lets bridges form between distinct objects.
Practitioners commonly employ two approaches to mitigating these problems: filtering the data and modifying the value criterion. In the former, a smoothing operator (e.g., mean or median filter) is applied in an attempt to remove this noise. This approach tends to destructively modify voxels around the interfaces that may be important. In the latter, the user performs a number of separate analyses across a range of eligibility criteria. This approach essentially considers the data as noise-free and the threshold value uncertain. One example of this approach is described in U.S. Pat. No. 5,832,103 to Giger, et al. A petroleum example of the second approach is U.S. patent application Ser. No. 10/195,582 filed Jul. 15, 2002. Neither the filtering nor the varying-eligibility approach admits the possibility that the character of the noise may vary from location to location in the volume. Neither approach characterizes the uncertainty in the result (e.g., uncertainty in body size or connectivity between bodies).
Some image-segmentation strategies that are well behaved in the presence of noise (e.g., level set techniques) could be applied to connectivity analysis problems, but they too are deterministic. They do not communicate the range of possibilities given the noise in the data.
The above-described technologies are based on established image-processing techniques. They address connectivity and size, but not uncertainty. There are uncertainty-aware techniques for estimating the connectivity and size of a geologic body in 3-D that are not based on image analysis. These use Monte Carlo techniques to produce multiple realizations of a geologic model that “honors” modeled uncertainty in stratigraphy, object geometries, rock properties, and other model variables. The difference between these techniques (embodied in the JACTA add-in to the commercial software product, “gOcad”, to name one example) is that the uncertainty in connectivity and size is a side effect of the integration of many forms of uncertainty, some of which are rarely adequately characterized or integrated. In other words, the uncertainty in connectivity and size is attributed to the secondary effects of modeling uncertainties, not directly to the primary source of uncertainty: the noise in the observed data. What is needed is a technique that directly estimates uncertainty in connectivity and size from the measured statistical properties of a densely sampled dataset. The present invention satisfies this need.